On the Perturbative Equivalence Between the Hamiltonian and Lagrangian Quantizations

TL;DR

This paper proves the perturbative equivalence of Hamiltonian and Lagrangian quantization schemes, demonstrating that the quantum master equation admits a local formal solution, thus bridging two fundamental approaches in quantum field theory.

Contribution

It establishes the perturbative equivalence between Hamiltonian and Lagrangian quantizations and shows the existence of a local formal solution to the quantum master equation.

Findings

Hamiltonian and Lagrangian quantizations are perturbatively equivalent.

The quantum master equation has a local formal solution.

The equivalence is demonstrated within the perturbative framework.

Abstract

The Hamiltonian (BFV) and Lagrangian (BV) quantization schemes are proved to be equivalent perturbatively to each other. It is shown in particular that the quantum master equation being treated perturbatively possesses a local formal solution.